Analysis of imaging for laser triangulation sensors under Scheimpflug rule.

In this work a detailed analysis of the problem of imaging of objects lying in the plane tilted with respect to the optical axis of the rotationally symmetrical optical system is performed by means of geometrical optics theory. It is shown that the fulfillment of the so called Scheimpflug condition (Scheimpflug rule) does not guarantee the sharp image of the object as it is usually declared because of the fact that due to the dependence of aberrations of real optical systems on the object distance the image becomes blurred. The f-number of a given optical system also varies with the object distance. It is shown the influence of above mentioned effects on the accuracy of the laser triangulation sensors measurements. A detailed analysis of laser triangulation sensors, based on geometrical optics theory, is performed and relations for the calculation of measurement errors and construction parameters of laser triangulation sensors are derived.